X-ray or gamma ray systems or devices – Specific application – Diffraction – reflection – or scattering analysis
Reexamination Certificate
2001-08-22
2003-05-13
Church, Craig E. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Diffraction, reflection, or scattering analysis
C378S086000
Reexamination Certificate
active
06563906
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to density measurement using Compton scattering of X-rays for determining density at a point within an object without exposing the entire object to radiations. This invention also pertains to formulating an algorithm for solving density-measurement equations.
BACKGROUND OF THE INVENTION
In nondestructive evaluation, it is often needed to know the density at a point, or points, in a region of interest within an object. Point-density measurement is useful, for instance, to detect a flaw in an isolated over-stressed region of a component. In another example, when a suspect material is identified by radiography, point-by-point imaging can be used to determine the density of the suspect material without having to generate a point-by-point density image of the entire object. This can be useful, for example, in the detection of explosives and other contraband materials in passenger luggage. In medical applications, point-by-point imaging can be useful in follow-up examination to determine, for instance, whether treatment was effective in destroying an isolated tumor.
Measuring density at an isolated point within an object using a X-ray beam requires the beam to reach the point of interest, to pass through the point of interest and to reach a detector. In its way to the point of interest, the beam is modified as it transverses other points, unless the point of interest is at the surface of the object. The beam is modified again by the point of interest. The beam is further affected by other points as it travels out of the object toward the detector. For this reason, basically, conventional transmission radiographic imaging is not suited for obtaining the density at a point within an object, since radiography provides an integrated line density along the path of the radiation beam penetrating the object. To determine the density at a point, many multiple radiation exposures at different angles or different directions must be effected, with subsequent numerical image reconstruction. This process is often referred to as computed tomography. Such a complete imaging process is tedious and expensive. It involves numerous consecutive measurements using many measuring devices and complex reconstruction algorithms to generate the image.
Examples of related prior art using radiographic imaging processes are described in the following patent documents:
U.S. Pat. No. 3,809,904 issued on May 7, 1974 to Clarke et al.;
U.S. Pat. No. 4,123,654 issued on Oct. 31, 1978 to Reiss et al.;
U.S. Pat. No. 4,228,351 issued on Oct. 14, 1980 to Snow et al.;
U.S. Pat. No. 4,768,214 issued on Aug. 30, 1988 to P. J. Bjorkholm;
U.S. Pat. No. 4,850,002 issued on Jul. 18, 1989 to Harding et al.;
U.S. Pat. No. 4,887,285 issued on Dec. 12, 1989 to Harding et al.;
U.S. Pat. No. 5,247,560 issued on Sept. 21, 1993 to Hosokama et al.;
U.S. Pat. No. 5,247,561 issued on Sept. 21, 1993 to A. F. Kotowski;
U.S. Pat. No. 5,696,806 issued on Dec. 9, 1997 to Grodzins et al.;
CA 1,101,133 issued on May 12,1981 to G. Harding;
CA 1,135,878 issued on Nov. 16, 1982 to Jatteau et al.;
CA 1,157,968 issued on Nov. 29, 1983 to Harding et al.
In the methods of the prior art, the attenuation of the radiation along the path of the X-ray beam is in most cases estimated, extrapolated from previous measurements or considered as a constant. It is believed that these estimations and extrapolations could lead to measurement inaccuracies, and for this reason, basically, it is believed that the prior art methods have only been used with limited degrees of success. As such, it may be appreciated that there continues to be a need for a method to determine with precision the density at a point, or points in a region of interest within an object, without performing a complete imaging of the object.
Before describing the present invention, however, it is deemed that certain general information should be reminded in order to afford a clearer understanding of the following specification. In particular, a general knowledge of the Compton scattering principle applicable to a X-ray beam is believed essential to facilitate the understanding of the present invention.
Compton scattering is the incoherent collision between photons and the free electrons of the atoms and it dominates all other photon interactions. Since Compton scattering is an interaction with the electrons of the atom, its probability of interaction depends on the density of the medium. Therefore, Compton scattering principle is available for non-destructive measurement of density.
In order to demonstrate how Compton scattering principle can be used to measure the density at a point within an object, reference is firstly made to
FIG. 1
where a source of X-ray having an energy E is placed at point P
s
and is directed at a small voxel V located at point P
v
within an object O. A detector is placed at point P
d
to determine the electron density of the voxel ‘V’. In order for the detector at point P
d
to monitor the scattered radiation E′ from point P
v
it must be collimated so that it focuses along the direction P
v
-P
d
. The unique relationship between the scattered photon energy E′, and the scattering angle &thgr; is expressed as follows:
E′=E
/(1+((
E/m
o
c
2
)(1−cos &thgr;))) (1)
where E is the initial energy of the incident photon, and m
o
c
2
is the rest mass of the electron (511 keV). With the detector field-of-view focused on the scatter line along P
v
-P
d
and the source collimated along the direction of P
s
-P
v
the electron density, &rgr;
e
v
at P
v
can be related to the detector response, S(E,&thgr;) as follows:
S
(
E
,&thgr;)
=k
(
E
,&thgr;)
f
l
&rgr;
e
v
f
s
(2)
where f
l
and f
s
are attenuation factors which account for the decrease in photon intensity as radiation travels toward and away from the scattering point, that is between the points P
in
-P
v
and between the points P
v
-P
out
respectivelly. k(E,&thgr;) is a system constant that can be expressed, for a well-collimated source, as
k
(
E
,&thgr;)=
S
0
D
&sgr;(
E
)(
p
(cos &thgr;)/2&pgr;
R
2
)&eegr;(
E
′) (3)
where S
0
is the source strength per unit area, D is voxel width, &sgr;(E) is the probability of scattering per unit area per electron (called microscopic scattering cross section) at energy E, p(cos &thgr;) is the probability of a photon scattered at a specific angle &thgr;, R is the distance from the scattering point to the detector, and &eegr;(E′) is the detector efficiency at energy E′.
The incident and scattering attenuation factors (f
l
and f
s
) can be expressed as
f
i
=
exp
[
-
∫
Pin
Pr
μ
t
(
r
,
E
)
ⅆ
r
]
=
exp
[
-
∫
Pin
Pv
σ
t
(
r
,
E
)
ρ
e
(
r
)
ⅆ
r
]
and
(
4
)
f
s
=
exp
[
-
∫
Pv
Pout
μ
t
(
r
′
,
E
′
)
ⅆ
r
′
]
=
exp
[
-
∫
Pv
Pout
σ
t
(
r
′
,
E
′
)
ρ
e
(
r
′
)
ⅆ
r
′
]
(
5
)
where &mgr;
t
(r,E) is the linear attenuation coefficient of photon of energy E at point (r), &rgr;
e
(r) is the electron density at point (r) along the beam path, and &sgr;
t
(r,E) is the total attenuation cross-section of photon of energy E per unit electron density by the material at point (r).
It will be appreciated that in order to calculate the electron density from the detector response, S(E,&thgr;), as shown in equation (2), the attenuation factors, f
l
and f
s
must be determined. This has created problems in the past, since the values of these factors depend on the density of the material present in the path of the radiation beam, which are not usually known. Consequently, the formulat
Achmad Balza
Hussein Esam
Church Craig E.
Theriault Mario
University of New Brunswick
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